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Fourth stop: A dive into mathematical logic
February 9th, 2009 by dholm

This is the fourth installment in my Amazon Marketplace spending spree.

Back in school we used the horrible book “Grundläggande Logik” (eng. Basic Logic) by Kaj B. Hansen in the mathematical logics course. This book appears to be an experiment in cross-referencing chapters back and forth and informing the reader that several of the basic concepts presented are trivial and hence not explained. Even the professor we had didn’t like the book but he said that there was no better book on the subject which I later learnt should be interpreted as “there is no better book in Swedish on the subject“. I did not do too well in that course.

Recently I read the illuminating blog entry “Math For Programmers” by Steve Yegge. The following two books were recommended in the comments section and I found them at a great price so I ordered them on the spot.

Computability and Logic by George S. Boolos et. al.

Computability and Logic by George S. Boolos et. al.

Logic for Mathematicians by A.G. Hamilton

Logic for Mathematicians by A.G. Hamilton


One Response  
  • Kaj B Hansen writes:
    July 9th, 200917:57at

    TO: David Holm
    FROM: Kaj Börge Hansen
    2009-07-09

    Dear Sir:

    I read with great interest your review of the textbook “Grundläggande logik”. You have three critical comments.

    (1) The book appears to be an experiment in cross-referencing chapters back and forth … .
    COMMENT:
    There are references back but not forth in the book. The back-references occur in examples which are developments of an earlier example. The alternative should be to repeat the previous example. Such a procedure should annoy several of the readers. And worse: It should not be accepted by the publisher because then the book should have been 50-100 pp. longer than it actually is, and every page means an extra cost for the publisher during the production of the book. I had some conflicts with the head of the computer literature section in Studentlitteratur because she thought that the first edition was too long (c. 350 pp.). I wanted many examples in the textbook and did not want to sacrifice any example for the possibility of making unnecessary iterations of text.

    (2) This book appears to be an exeperiment in (…) informing the reader that several of the basic concepts presented are trivial and hence not explained.
    REPLY:
    All basic concepts are precisely defined. All basic concepts are also carefully explained. The method of explanation used is mostly to apply the concepts in examples and thereby SHOW their impact and meaning. An alternative method of explanation used by many textbook writers is to talk at length about the concept in a persuasive tone; but I do not want such “pladder” in my textbook. If you have a taste for this type of pedagogy, I recommend Dag Prawitz’s “ABC i symbolisk logik”. One “drawback” about my method of explanation is that it demands of the students that they WORK with the examples. It is not a textbook for lazy students. Of course, I consider this an advantage and not a drawback at all. I have written my book in such a way that 15-25% of the students should be able to read it alone and learn logic from it by self-study. The remaining 75-85% weaker students need help from a teacher whose duty it is to supply whatever extra explanations are needed. My opinion is still that this is the right level at which to place such an introductory text.

    (3) “Grundläggande logik” is a horrible book.
    COMMENT:
    It is sad that the book does not suit you; but nobody can write a book which suits all readers. “Ingen kan vara alla till lags”. I have used the book ten times in the program of computer and system science at Uppsala University, 1992-2003, and three times in the IT-program at Åland Institute of Technology, 1999-2001. The results have always been good: High average quality on the student’s knowledge of logic after the course and a throughput of 90-95%. In the course evaluations at the end of the courses, the average grade given by the students to the book was every year in the range 3.5-3.7 on a scale running from 0 to 5. The individual comments ranged from “the best book I have ever read” to formulations similar to the ones you use.

    Concerning the two alternative textbook you mention: I have never seen “Computability and Logic” by Boolos, Burgess, and Jeffrey. The three authors are good logicians in the second division which may indicate with some probability, but not certainty, that the textbook is also good. In 1986, I was asked to teach a course on logic for computer science students at the University of Stockholm with Hamilton’s “Logic for Mathematicians” as textbook. I taught the course. Hamilton’s book CAN be used as a textbook in such a course; but I consider it the worst textbook of logic I have ever seen. (As a logician, Hamilton plays at best in the third division — which does not exclude that he might be able to write a good textbook.)

    Whatever you and your friends think and say about “Grundläggande logik”, I am proud of it.

    Sincerely yours,
    Kaj Börge Hansen
    Fil Dr, MS, MSc, Docent


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